Statistical analysis of potential fields from subsurface reliefs

Abstract

The characteristics of potential fields in the wave number domain from a subsurface relief which can be used to model the basement or large scale discontinuities such as Moho, Curie Point geotherm etc., are discussed. In a specific low wave band the spectrum of the potential fields is related to the spectrum of the relief through a simple exponential decay of the depth beyond which it is perturbed by higher order terms. The effect of the higher order terms on the spectrum for a gaussian distribution of the relief is analysed. The wave band within which the above linear relationship is valid depends primarily upon the ratio between the average width and the amplitude of the relief. If the spectrum of the relief decays with increasing wave number as is generally the case, the effect of this factor on the decay of the spectrum of magnetic field is balanced to some extent by the factor k (wave number) in the expression. However, in case of gravity this will result in a faster decay of the spectrum providing a higher depth estimate, which can either be corrected accordingly or can be regarded as an upper bound on the depth. Systematic model studies on deterministic models and simulated reliefs are described to examine the effects referred to above and to verify the reliability of the depth estimated from the computed spectrum of potential fields. Three kinds of relief, two generated from random numbers using a low-pass cosine filter from 10–20% and 5–10% of total frequency band, and the third, a very smooth relief drawn by hand, are used for the purpose. The spectrum of the magnetic field from the relief generated from random numbers shows a better linear relationship and other characteristics if it is divided by wave numbers ( k). The theory developed here is applied on the marine magnetic profile and regional Bouguer anomaly across the Faeroe-Shetland channel, and the results so obtained are discussed in terms of the subsurface crustal structure in the region.